Abstract: This paper investigates dynamic modeling, trajectory tracking control, and vibration suppression for space manipulator handling a flexible payload system based on a differential-algebraic equations framework. The flexible payload is selected as a flexible beam. The dynamic models for the flexible beam and the rigid space manipulator are established using the absolute nodal coordinate formulation and Lagrange’s equations, respectively. By incorporating constraint equations between the manipulator and the flexible beam, the system dynamic model is formulated as a set of differential-algebraic equations. To achieve trajectory tracking for the manipulator while suppressing the vibration of the flexible payload, a double-loop control strategy is designed. This strategy integrates model predictive control with a low-frequency update rate and prescribed performance control with a high-frequency update rate. Stability analysis demonstrates the convergence of the closed-loop system. Furthermore, numerical simulations and experimental results obtained using a QArm manipulator validate the effectiveness of the proposed control strategy.